پیش‌بینی آسیب ناشی از ضربه سرعت آهسته بر ورق های کامپوزیتی لایه ای
نویسندگان
گروه مهندسی مکانیک، دانشگاه زنجان، زنجان
چکیده
در این پژوهش، یک مدل المان محدود برای تحلیل ضربه سرعت پایین بر ورق کامپوزیتی ارائه شده است و با استفاده از آن آسیب ایجاد شده ناشی از برخورد یک ضربه‌زننده، با ورق کامپوزیتی لایه‌ای با سرعت پایین، مورد بررسی قرار گرفته است. برای پیش‌بینی آسیب از تئوری پیشنهاد شده توسط چویی- چانگ و همچنین معیار سای- هیل استفاده شده است. برای مدل‌سازی و تحلیل رفتار ورق از تئوری مرتبه اول برشی و تئوری المان محدود ریتز و برای مدل‌سازی تماس از قانون تماس اصلاح‌شده هرتز استفاده شده است. برای حل زمانی معادلات حرکت ورق و ضربه‌زننده از روش انتگرال‌گیری نیومارک استفاده شده است. در قسمت نتایج عددی شرایط مرزی مختلف، ابعاد مختلف و لایه‌گذاری متفاوت مورد بررسی قرار گرفته است و به بررسی آسیب ناشی از ضربه سرعت پایین در ورق کامپوزیتی لایه‌ای پرداخته شده است. پارامتر آسیب و ناحیه آسیب ناشی از ضربه، مورد بررسی قرار گرفته است و اثر پارامترهای مختلف بررسی شده است.
کلیدواژه‌ها
عنوان مقاله [English]
Low Velocity Impact Damage Prediction in Laminated Composite Plates
نویسندگان [English]
- I. Ahmadi
- D. Kouhbor
- R. Taghiloo
In this paper, a finite element model is presented for the transient analysis of low velocity impact, and the impact induced damage in the composite plate subjected to low velocity impact is studied. The failure criteria suggested by Choi and Chang and the Tsai-Hill failure criteria are used for the prediction of the damage in the composite plate; then the effect of various parameters on the impact induced damage is investigated. The first order shear deformation plate theory and the Ritz finite element method are employed for modeling the behavior of plate, and the modified Hertz contact low is used for the prediction of the contact force through the impact. In the numerical results, the time history of indentation, contact force and stress during the impact and the impact induced damage is investigated. The matrix cracking and delamination in the plies of the laminated composite plate subjected to low velocity impact are studied and the effects of various parameters are investigated.
کلیدواژه‌ها [English]
- Impact Damage Prediction
- Low Velocity Impact
- Finite element analysis
- Modified Hertz Contact Law
- Mindlin Plate Theory
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2. Bose, P., and Reddy, J. N., “Analysis of Composite Plates using Various Plate Theories. Part 2: Finite Element Model and Numerical Results”, Structural Engineering and Mechanics, Vol. 6, No. 7, pp. 727-746, 1998.
3. Soldatos, K. P., and Watson, P., “A Method for Improving the Stress Analysis Performance of Two-Dimensional Theories for Composite Laminates”, Acta Mechanica, Vol. 123, pp. 163-186, 1997.
4. Soldatos, K. P., and Watson, P., “Accurate Stress Analysis of Laminated Plates Combining a Two-Dimensional Theory with the Exact Three-Dimensional Solution for Simply Supported Edges”, Mathematics and Mechanics of Solids, Vol. 2, pp. 459-489, 1997.
5. Shu, X. P., and Soldatos, K. P., “Cylindrical Bending of Angle-Ply Laminates Subjected to Different Sets of Edge Boundary Conditions”, International Journal of Solids and Structures, Vol. 37, pp. 4289-4307, 2000.
6. Abrate, S., “Impact on Laminated Composites, Recent Advances”, Applied Mechanics Review, Vol. 47, pp. 517-544, 1994.
7. Abrate, S., Impact on Composite Structures, New York, Cambridge University Press, 1998.
8. Cantwell, W. J., and Morton, J., “The Impact Resistance of Composite Materials- A Review”, Journal of Composite Structures, Vol. 22, pp. 347-362, 1991.
9. Pierson, M. O., and Vaziri, R., “Analytical Solution for Low-Velocity Impact Response of Composite Plates”, AIAA Journal, Vol. 34, pp. 1633-1640, 1996.
10. Michelle, S., Fatt, H., and Park, S., “Dynamic Models for Low-Velocity Impact Damage of Composite Sandwich Panel-Part B: Damage Initiation”, Journal of Composite Structures, Vol. 52, No. 3, pp. 353-364, 2001
11. Khalili, M. R., Malekzadeh, K., and Mittal, R. K., “A New Approach to Static and Dynamic Analysis of Composite Plates with Different Boundary Conditions”, Journal of Composite Structures, Vol. 69, pp. 149-155, 2005.
12. Choi, I. H., and Lim, C. H., “Low-Velocity Impact Analysis of Composite Laminates using Linearized Contact Law”, Journal of Composite Structures, Vol. 66, pp. 125-132, 2004.
13. Roy, T., and Chakraborty, D., “Delamination in Hybrid FRP Laminates under Low Velocity Impact”, Journal of Reinforced Plastics and Composites, Vol. 25, pp. 1939-1956, 2006.
14. Zhang, Y., Zhu, P., and Lai, X., “Finite Element Analysis of Low-Velocity Impact Damage in Composite Laminated Plate”, Materials and Design, Vol. 27, pp. 513-519, 2006.
15. Tiberkak, R., Bachene, M., Rechak, S., and Necib, B., “Damage Prediction in Composite Plates Subjected to Low Velocity Impact”, Composite Structures, Vol. 83, pp. 73-82, 2008.
16. Choi, I., H.,“Low-Velocity Impact Analysis of Composite Laminates under Initial in-Plane Load”, Composite Structures, Vol. 86, pp. 251-257, 2008.
17. Choudhary, S. S., and Tungikar, V. B., “A Simple Finite Element for Nonlinear Analysis of Composite Plates”, International Journal of Engineering Science and Technology, Vol. 3, No. 6, pp. 4897-4907, 2011.
18. Sabouri, H., Ahmadi, H., and Liaghat, C. H., “Ballistic Impact Perforation Into Glare Target: Experiment, Numerical Modeling and Investigation of Aluminium Stacking Sequence”, International Journal Vehicle Structures & Systems, Vol. 3, pp. 178-183, 2011.
19. Khalili, S. M. R., Soroush, M., Davar, A., and Rahmani, O., “Finite Element Modeling of Low-Velocity Impact on Laminated Composite Plates and Cylindrical Shells”, Composite Structures, Vol. 93, pp. 1363-1375, 2011.
20. Xiao, Sh., Chen, P., Ye and Q., “Prediction of Damage Area in Laminated Composite Plates Subjected to Low Velocity Impact”, Composites Science and Technology, Vol. 98, pp. 51-56, 2014.
21. Hassan, M. A., Naderi, S., and Bushroa, A. R., “Low-Velocity Impact Damage of Woven Fabric Composites: Finite Element Simulation and Experimental Verification”, Materials & Design, Vol. 53, pp. 706-718, 2014.
22. Yang, B., Wang, Z., Zhou, L., Zhang, J., and Liang, W., “Experimental and Numerical Investigation of Interply Hybrid Composites Based on Woven Fabrics and PCBT Resin Subjected to Low-Velocity Impact”, Composite Structures, Vol. 132, pp. 464-476, 2015.
23. Patil, S., Reddy, D. M., and Reddy, M., “Low Velocity Impact Analysis on Composite Structures - A Review”, AIP Conference Proceedings, Vol. 1943, pp. 020009-1-9, 2018.
24. Tam, T. M., and Sun, C. T., Wave Propagation in Graphite/Epoxy Laminates Due to Impact, NASA CR, 1982.
25. Newmark, N. M., “A Method of Computation for Structural Dynamic”, Journal of Engineering Mechanics Division, Vol. 85, pp. 67-84, 1959.
26. Sun, C. T., and Chen, J. K., “On the Impact of Initially Stressed Composite Laminates”, Journal of Composite Materials, Vol. 19, pp. 490-504, 1985.
27. Tiberkak, R., Bachene, M., Rechak, S., and Necib, B., “Damage Prediction in Composite Plates Subjected to Low Velocity Impact”, Composite Structures, Vol. 83, pp. 73-82, 2008.
28. Naik, N. K., Chandra Sekher, Y., and Sailendra, M., “Damage in Woven Fabric Composites Subjected to Low-Velocity Impact”, Aerospace Engineering Department, Indian Institute of Technology, Vol. 400 , pp. 731-744, 2000.
29. Hill, R., The Mathematical Theory of Plasticity, Oxford University Press, London, 1950.
30. Tsai, S. W., Strength Theories of Filamentary Structures in Fundamental Aspects of Fiber Reinforced Plastic Composites, Wiley Interscience, New York, 1968.
31. Autar, K., Mechanics of Composite Material, CRC Press, 2nd ed, 2006.
32. Choi, H. Y., and Chang, F. K., “A Model for Predicting Damage in Graphite/ Epoxy Laminated Composites Resulting From Low-Velocity Point Impact”, Journal of Composite Materials, Vol. 26, pp. 2134-2169, 1992.
2. Bose, P., and Reddy, J. N., “Analysis of Composite Plates using Various Plate Theories. Part 2: Finite Element Model and Numerical Results”, Structural Engineering and Mechanics, Vol. 6, No. 7, pp. 727-746, 1998.
3. Soldatos, K. P., and Watson, P., “A Method for Improving the Stress Analysis Performance of Two-Dimensional Theories for Composite Laminates”, Acta Mechanica, Vol. 123, pp. 163-186, 1997.
4. Soldatos, K. P., and Watson, P., “Accurate Stress Analysis of Laminated Plates Combining a Two-Dimensional Theory with the Exact Three-Dimensional Solution for Simply Supported Edges”, Mathematics and Mechanics of Solids, Vol. 2, pp. 459-489, 1997.
5. Shu, X. P., and Soldatos, K. P., “Cylindrical Bending of Angle-Ply Laminates Subjected to Different Sets of Edge Boundary Conditions”, International Journal of Solids and Structures, Vol. 37, pp. 4289-4307, 2000.
6. Abrate, S., “Impact on Laminated Composites, Recent Advances”, Applied Mechanics Review, Vol. 47, pp. 517-544, 1994.
7. Abrate, S., Impact on Composite Structures, New York, Cambridge University Press, 1998.
8. Cantwell, W. J., and Morton, J., “The Impact Resistance of Composite Materials- A Review”, Journal of Composite Structures, Vol. 22, pp. 347-362, 1991.
9. Pierson, M. O., and Vaziri, R., “Analytical Solution for Low-Velocity Impact Response of Composite Plates”, AIAA Journal, Vol. 34, pp. 1633-1640, 1996.
10. Michelle, S., Fatt, H., and Park, S., “Dynamic Models for Low-Velocity Impact Damage of Composite Sandwich Panel-Part B: Damage Initiation”, Journal of Composite Structures, Vol. 52, No. 3, pp. 353-364, 2001
11. Khalili, M. R., Malekzadeh, K., and Mittal, R. K., “A New Approach to Static and Dynamic Analysis of Composite Plates with Different Boundary Conditions”, Journal of Composite Structures, Vol. 69, pp. 149-155, 2005.
12. Choi, I. H., and Lim, C. H., “Low-Velocity Impact Analysis of Composite Laminates using Linearized Contact Law”, Journal of Composite Structures, Vol. 66, pp. 125-132, 2004.
13. Roy, T., and Chakraborty, D., “Delamination in Hybrid FRP Laminates under Low Velocity Impact”, Journal of Reinforced Plastics and Composites, Vol. 25, pp. 1939-1956, 2006.
14. Zhang, Y., Zhu, P., and Lai, X., “Finite Element Analysis of Low-Velocity Impact Damage in Composite Laminated Plate”, Materials and Design, Vol. 27, pp. 513-519, 2006.
15. Tiberkak, R., Bachene, M., Rechak, S., and Necib, B., “Damage Prediction in Composite Plates Subjected to Low Velocity Impact”, Composite Structures, Vol. 83, pp. 73-82, 2008.
16. Choi, I., H.,“Low-Velocity Impact Analysis of Composite Laminates under Initial in-Plane Load”, Composite Structures, Vol. 86, pp. 251-257, 2008.
17. Choudhary, S. S., and Tungikar, V. B., “A Simple Finite Element for Nonlinear Analysis of Composite Plates”, International Journal of Engineering Science and Technology, Vol. 3, No. 6, pp. 4897-4907, 2011.
18. Sabouri, H., Ahmadi, H., and Liaghat, C. H., “Ballistic Impact Perforation Into Glare Target: Experiment, Numerical Modeling and Investigation of Aluminium Stacking Sequence”, International Journal Vehicle Structures & Systems, Vol. 3, pp. 178-183, 2011.
19. Khalili, S. M. R., Soroush, M., Davar, A., and Rahmani, O., “Finite Element Modeling of Low-Velocity Impact on Laminated Composite Plates and Cylindrical Shells”, Composite Structures, Vol. 93, pp. 1363-1375, 2011.
20. Xiao, Sh., Chen, P., Ye and Q., “Prediction of Damage Area in Laminated Composite Plates Subjected to Low Velocity Impact”, Composites Science and Technology, Vol. 98, pp. 51-56, 2014.
21. Hassan, M. A., Naderi, S., and Bushroa, A. R., “Low-Velocity Impact Damage of Woven Fabric Composites: Finite Element Simulation and Experimental Verification”, Materials & Design, Vol. 53, pp. 706-718, 2014.
22. Yang, B., Wang, Z., Zhou, L., Zhang, J., and Liang, W., “Experimental and Numerical Investigation of Interply Hybrid Composites Based on Woven Fabrics and PCBT Resin Subjected to Low-Velocity Impact”, Composite Structures, Vol. 132, pp. 464-476, 2015.
23. Patil, S., Reddy, D. M., and Reddy, M., “Low Velocity Impact Analysis on Composite Structures - A Review”, AIP Conference Proceedings, Vol. 1943, pp. 020009-1-9, 2018.
24. Tam, T. M., and Sun, C. T., Wave Propagation in Graphite/Epoxy Laminates Due to Impact, NASA CR, 1982.
25. Newmark, N. M., “A Method of Computation for Structural Dynamic”, Journal of Engineering Mechanics Division, Vol. 85, pp. 67-84, 1959.
26. Sun, C. T., and Chen, J. K., “On the Impact of Initially Stressed Composite Laminates”, Journal of Composite Materials, Vol. 19, pp. 490-504, 1985.
27. Tiberkak, R., Bachene, M., Rechak, S., and Necib, B., “Damage Prediction in Composite Plates Subjected to Low Velocity Impact”, Composite Structures, Vol. 83, pp. 73-82, 2008.
28. Naik, N. K., Chandra Sekher, Y., and Sailendra, M., “Damage in Woven Fabric Composites Subjected to Low-Velocity Impact”, Aerospace Engineering Department, Indian Institute of Technology, Vol. 400 , pp. 731-744, 2000.
29. Hill, R., The Mathematical Theory of Plasticity, Oxford University Press, London, 1950.
30. Tsai, S. W., Strength Theories of Filamentary Structures in Fundamental Aspects of Fiber Reinforced Plastic Composites, Wiley Interscience, New York, 1968.
31. Autar, K., Mechanics of Composite Material, CRC Press, 2nd ed, 2006.
32. Choi, H. Y., and Chang, F. K., “A Model for Predicting Damage in Graphite/ Epoxy Laminated Composites Resulting From Low-Velocity Point Impact”, Journal of Composite Materials, Vol. 26, pp. 2134-2169, 1992.
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